Reducibility among Fractional Stability Problems

— In a landmark paper [32], Papadimitriou introduced a number of syntactic subclasses of TFNP based on proof styles that (unlike TFNP) admit complete problems. A recent series of results [11], [16], [5], [6], [7], [8] has shown that finding Nash equilibria is complete for PPAD, a particularly notable subclass of TFNP. A major goal of this work is to expand the universe of known PPAD-complete problems. We resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance: Fractional Stable Paths Problem (FSPP) [18] - Internet routing; Core of Balanced Games [34] - Economics and Game theory; Scarf’s Lemma [34] Combinatorics; Hypergraph Matching [1]- Social Choice and Preference Systems; Fractional Bounded Budget Connection Games (FBBC) [26] - Social networks; and Strong Fractional Kernel [2]Graph Theory. In fact, we show that no fully po...

• Type: Conference
• Year: 2009
• Where: FOCS
• Authors: Shiva Kintali, Laura J. Poplawski, Rajmohan Rajaraman, Ravi Sundaram, Shang-Hua Teng
• Keywords: Admit Complete Problems, FOCS 2009, Personalized Equilibria, Preference Games, Theoretical Computer Science